A Class of New Pouzet-Runge-Kutta-Type Methods for Nonlinear Functional Integro-Differential Equations

Table 2

(a) The errors of the numerical solutions of (2.22) by methods {(7.1), (3.10)}, (b) The CPU times (in second) of methods (3.7)–(3.10) for (2.23) and (c) The CPU times (in second) of methods {(7.1), (3.10)} for (2.23).

(a)

(Δ𝑣,ℎ)	Gauss	Radau IA	Radau IIA	Lobatto IIIC
(𝜋/30,√3/16)	9.0193𝑒−006	3.7273𝑒−004	3.8966𝑒−004	1.4083𝑒−002
(𝜋/60,√3/32)	5.6739𝑒−007	4.6491𝑒−005	4.9558𝑒−005	3.5453𝑒−003
(𝜋/120,√3/64)	3.5534𝑒−008	5.7933𝑒−006	6.2360𝑒−006	8.8912𝑒−004
(𝜋/240,√3/128)	2.2217𝑒−009	7.2284𝑒−007	7.8186𝑒−007	2.2261𝑒−004

(b)

(Δ𝑣,ℎ)	Gauss	Radau IA	Radau IIA	Lobatto IIIC
(𝜋/30,√3/16)	7.0780𝑒+000	6.8750𝑒+000	6.9060𝑒+000	6.9380𝑒+000
(𝜋/60,√3/32)	4.4468𝑒+001	4.4500𝑒+001	4.4766𝑒+001	4.5172𝑒+001
(𝜋/120,√3/64)	3.3039𝑒+002	3.3156𝑒+002	3.3281𝑒+002	3.3264𝑒+002
(𝜋/240,√3/128)	2.7117𝑒+003	2.7042𝑒+003	2.7109𝑒+003	2.7291𝑒+003

(c)

(Δ𝑣,ℎ)	Gauss	Radau IA	Radau IIA	Lobatto IIIC
(𝜋/30,√3/16)	4.2180𝑒+000	4.2350𝑒+000	4.2650𝑒+000	4.2820𝑒+000
(𝜋/60,√3/32)	3.0953𝑒+001	3.0234𝑒+001	3.1031𝑒+001	3.1125𝑒+001
(𝜋/120,√3/64)	2.7055𝑒+002	2.8400𝑒+002	2.7213𝑒+002	2.7105𝑒+002
(𝜋/240,√3/128)	2.7821𝑒+003	2.8164𝑒+003	2.7950𝑒+003	2.8006𝑒+003